Journal of Systems Engineering and Electronics ›› 2007, Vol. 18 ›› Issue (4): 871-878.

• CONTROL THEORY AND APPLICATION • Previous Articles     Next Articles

Robust decentralized H∞ control of multi-channel systemswith norm-bounded parametric uncertainties

Chen Ning & Gui Weihua   

  1. School of Information Science and Engineering, Central South Univ., Changsha 410083, P.R. China
  • Online:2007-12-24 Published:2010-01-03


A robust decentralized H∞ control problem for uncertain multi-channel systems is considered. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in both the system and control input matrices. The dynamic output feedback is mainly dealt with. A necessary and sufficient condition for the uncertain multi-channel system to be stabilized robustly with a speci ed disturbance attenuation level is derived based on the bounded real lemma, which is reduced to a feasibility problem of a nonlinear matrix inequality (NMI). A two-stage homotopy method is used to solve the NMI iteratively. First, a decentralized controller for the nominal system with no uncertainty is computed by imposing structural constraints on the coefficient matrices of the controller gradually. Then the decentralized controller is modified, again gradually, to cope with the uncertainties. On each stage, a variable is fixed alternately at the iterations to reduce the NMI to a linear matrix inequality (LMI). A given example shows the efficiency of this method.